%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:01:21 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.64s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 12
% Syntax : Number of clauses : 296 ( 296 unt; 0 nHn; 242 RR)
% Number of literals : 296 ( 295 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c2,axiom,
uu = f(u,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
f(u3,uu) = f(u3,f(u,u)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
cnf(c5,plain,
f(u,f(n3,X2)) = f(f(u,n3),f(u,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
f(u,n3) = u3,
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
f(f(u,n3),f(u,X2)) = f(u3,f(u,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
f(u,f(n3,X2)) = f(u3,f(u,X2)),
inference(transitivity,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
f(u,f(n3,u)) = f(u3,f(u,u)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
f(u3,f(u,u)) = f(u,f(n3,u)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
f(n1,n2) = f(n1,f(n1,n1)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
f(n2,f(n1,X2)) = f(f(n1,n1),f(n1,X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c15,plain,
f(n1,f(n1,X2)) = f(f(n1,n1),f(n1,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c16,plain,
f(f(n1,n1),f(n1,X2)) = f(n1,f(n1,X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
f(n2,f(n1,X2)) = f(n1,f(n1,X2)),
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
f(n2,f(n1,n1)) = f(n1,f(n1,n1)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
f(n1,f(n1,n1)) = f(n2,f(n1,n1)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[c12]) ).
cnf(c21,plain,
f(n2,f(n1,n1)) = f(n2,n2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c23,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
f(n2,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
f(n1,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
f(n1,n2) = u,
inference(transitivity,[status(thm)],[c13,c25]) ).
cnf(c27,plain,
u = f(n1,n2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
f(n2,u) = f(n2,f(n1,n2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
f(n2,f(n1,n2)) = f(n1,f(n1,n2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c30,plain,
f(n1,f(n1,n2)) = f(n1,u),
inference(congruence,[status(thm)],[c26]) ).
cnf(c31,plain,
f(n2,f(n1,n2)) = f(n1,u),
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
f(n2,u) = f(n1,u),
inference(transitivity,[status(thm)],[c28,c31]) ).
cnf(c33,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
u = f(n1,n2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c35,plain,
f(n2,u) = f(n2,f(n1,n2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
f(n2,f(n1,X2)) = f(f(n2,n1),f(n2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c37,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c38,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
f(f(n2,n1),f(n2,X2)) = f(n3,f(n2,X2)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
f(n2,f(n1,X2)) = f(n3,f(n2,X2)),
inference(transitivity,[status(thm)],[c36,c39]) ).
cnf(c41,plain,
f(n2,f(n1,n2)) = f(n3,f(n2,n2)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c43,plain,
f(n3,f(n2,n2)) = f(n3,u),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
f(n2,u) = f(n3,u),
inference(transitivity,[status(thm)],[c35,c44]) ).
cnf(c46,plain,
f(n1,u) = f(n3,u),
inference(transitivity,[status(thm)],[c33,c45]) ).
cnf(c47,plain,
f(n3,u) = f(n1,u),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
f(u,f(n3,u)) = f(u,f(n1,u)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
f(u,f(n1,X2)) = f(f(u,n1),f(u,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c50,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c51,plain,
f(u,n1) = u1,
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
f(f(u,n1),f(u,X2)) = f(u1,f(u,X2)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
f(u,f(n1,X2)) = f(u1,f(u,X2)),
inference(transitivity,[status(thm)],[c49,c52]) ).
cnf(c54,plain,
f(u,f(n1,u)) = f(u1,f(u,u)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c56,plain,
f(u1,f(u,u)) = f(u1,uu),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
f(u,f(n1,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
f(u,f(n3,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c48,c57]) ).
cnf(c59,plain,
f(u3,f(u,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c11,c58]) ).
cnf(c60,plain,
f(u3,uu) = f(u1,uu),
inference(transitivity,[status(thm)],[c3,c59]) ).
cnf(c61,plain,
f(u1,uu) = f(u3,uu),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
f(n3,u) = f(n1,u),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c63,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c64,plain,
f(n2,u) = f(n2,f(n2,n2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c65,plain,
f(u,f(n2,X2)) = f(f(n2,n2),f(n2,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c66,plain,
f(n2,f(n2,X2)) = f(f(n2,n2),f(n2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c67,plain,
f(f(n2,n2),f(n2,X2)) = f(n2,f(n2,X2)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
f(u,f(n2,X2)) = f(n2,f(n2,X2)),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
f(u,f(n2,n2)) = f(n2,f(n2,n2)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
f(n2,f(n2,n2)) = f(u,f(n2,n2)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c72,plain,
f(u,f(n2,n2)) = f(u,u),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c74,plain,
f(u,f(n2,n2)) = uu,
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
f(n2,f(n2,n2)) = uu,
inference(transitivity,[status(thm)],[c70,c74]) ).
cnf(c76,plain,
f(n2,u) = uu,
inference(transitivity,[status(thm)],[c64,c75]) ).
cnf(c77,plain,
f(n1,u) = uu,
inference(transitivity,[status(thm)],[c63,c76]) ).
cnf(c78,plain,
f(n3,u) = uu,
inference(transitivity,[status(thm)],[c62,c77]) ).
cnf(c79,plain,
uu = f(n3,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
f(u,uu) = f(u,f(n3,u)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
f(u,f(n3,u)) = f(u3,f(u,u)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c82,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c83,plain,
f(u3,f(u,u)) = f(u3,uu),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
f(u,f(n3,u)) = f(u3,uu),
inference(transitivity,[status(thm)],[c81,c83]) ).
cnf(c85,plain,
f(u,uu) = f(u3,uu),
inference(transitivity,[status(thm)],[c80,c84]) ).
cnf(c86,plain,
f(u3,uu) = f(u,uu),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
f(u,uu) = f(u,f(u,u)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c88,plain,
f(u,f(u,X2)) = f(f(u,u),f(u,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c89,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c90,plain,
f(f(u,u),f(u,X2)) = f(uu,f(u,X2)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
f(u,f(u,X2)) = f(uu,f(u,X2)),
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
f(u,f(u,u)) = f(uu,f(u,u)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c94,plain,
f(uu,f(u,u)) = f(uu,uu),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c96,plain,
f(uu,uu) = v,
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
f(uu,f(u,u)) = v,
inference(transitivity,[status(thm)],[c94,c96]) ).
cnf(c98,plain,
f(u,f(u,u)) = v,
inference(transitivity,[status(thm)],[c92,c97]) ).
cnf(c99,plain,
f(u,uu) = v,
inference(transitivity,[status(thm)],[c87,c98]) ).
cnf(c100,plain,
f(u3,uu) = v,
inference(transitivity,[status(thm)],[c86,c99]) ).
cnf(c101,plain,
f(u1,uu) = v,
inference(transitivity,[status(thm)],[c61,c100]) ).
cnf(c102,plain,
v = f(u1,uu),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
f(a,v) = f(a,f(u1,uu)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
f(u1,uu) = f(u3,uu),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c105,plain,
f(a,f(u1,uu)) = f(a,f(u3,uu)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
f(u3,uu) = f(u3,f(u,u)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c107,plain,
f(a,f(u3,uu)) = f(a,f(u3,f(u,u))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
f(n3,f(n3,X2)) = f(f(n3,n3),f(n3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c109,plain,
f(n3,n3) = f(n3,f(n2,n1)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c110,plain,
f(n2,f(n1,n1)) = f(n3,f(n2,n1)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c111,plain,
f(n3,f(n2,n1)) = f(n2,f(n1,n1)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[c12]) ).
cnf(c113,plain,
f(n2,f(n1,n1)) = f(n2,n2),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c115,plain,
f(n2,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
f(n3,f(n2,n1)) = u,
inference(transitivity,[status(thm)],[c111,c115]) ).
cnf(c117,plain,
f(n3,n3) = u,
inference(transitivity,[status(thm)],[c109,c116]) ).
cnf(c118,plain,
f(f(n3,n3),f(n3,X2)) = f(u,f(n3,X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
f(f(n3,n3),f(n3,X2)) = f(u3,f(u,X2)),
inference(transitivity,[status(thm)],[c118,c9]) ).
cnf(c120,plain,
f(n3,f(n3,X2)) = f(u3,f(u,X2)),
inference(transitivity,[status(thm)],[c108,c119]) ).
cnf(c121,plain,
f(n3,f(n3,u)) = f(u3,f(u,u)),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
f(u3,f(u,u)) = f(n3,f(n3,u)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
f(a,f(u3,f(u,u))) = f(a,f(n3,f(n3,u))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
f(n3,u) = f(n1,u),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c125,plain,
f(n3,f(n3,u)) = f(n3,f(n1,u)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
f(a,f(n3,f(n3,u))) = f(a,f(n3,f(n1,u))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c128,plain,
f(n3,f(n1,u)) = f(n3,f(n2,u)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
f(a,f(n3,f(n1,u))) = f(a,f(n3,f(n2,u))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
uu = f(n3,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c131,plain,
f(f(n3,X2),uu) = f(f(n3,X2),f(n3,u)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
f(n3,f(X2,u)) = f(f(n3,X2),f(n3,u)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c133,plain,
f(f(n3,X2),f(n3,u)) = f(n3,f(X2,u)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
f(f(n3,X2),uu) = f(n3,f(X2,u)),
inference(transitivity,[status(thm)],[c131,c133]) ).
cnf(c135,plain,
f(f(n3,n2),uu) = f(n3,f(n2,u)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
f(n3,f(n2,u)) = f(f(n3,n2),uu),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
f(a,f(n3,f(n2,u))) = f(a,f(f(n3,n2),uu)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
f(f(n3,n2),f(u2,X2)) = f(f(f(n3,n2),u2),f(f(n3,n2),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c139,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c140,plain,
f(f(n3,n2),u2) = a,
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
f(f(f(n3,n2),u2),f(f(n3,n2),X2)) = f(a,f(f(n3,n2),X2)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
f(f(n3,n2),f(u2,X2)) = f(a,f(f(n3,n2),X2)),
inference(transitivity,[status(thm)],[c138,c141]) ).
cnf(c143,plain,
f(f(n3,n2),f(u2,uu)) = f(a,f(f(n3,n2),uu)),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
f(a,f(f(n3,n2),uu)) = f(f(n3,n2),f(u2,uu)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
f(u2,uu) = f(u2,f(u,u)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c146,plain,
f(u,f(n2,X2)) = f(f(u,n2),f(u,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c147,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c148,plain,
f(u,n2) = u2,
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
f(f(u,n2),f(u,X2)) = f(u2,f(u,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
f(u,f(n2,X2)) = f(u2,f(u,X2)),
inference(transitivity,[status(thm)],[c146,c149]) ).
cnf(c151,plain,
f(u,f(n2,u)) = f(u2,f(u,u)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
f(u2,f(u,u)) = f(u,f(n2,u)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
f(u,f(n2,u)) = f(u,f(n1,u)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c154,plain,
f(u,f(n1,u)) = f(u1,f(u,u)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c155,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c156,plain,
f(u1,f(u,u)) = f(u1,uu),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
f(u,f(n1,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c154,c156]) ).
cnf(c158,plain,
f(u,f(n2,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c153,c157]) ).
cnf(c159,plain,
f(u2,f(u,u)) = f(u1,uu),
inference(transitivity,[status(thm)],[c152,c158]) ).
cnf(c160,plain,
f(u2,uu) = f(u1,uu),
inference(transitivity,[status(thm)],[c145,c159]) ).
cnf(c161,plain,
f(f(n3,n2),f(u2,uu)) = f(f(n3,n2),f(u1,uu)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
f(f(n3,n2),f(u1,uu)) = f(f(n3,n2),v),
inference(congruence,[status(thm)],[c101]) ).
cnf(c163,plain,
uu = f(n3,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c164,plain,
f(n3,uu) = f(n3,f(n3,u)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
f(n3,u) = f(n1,u),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c166,plain,
f(n3,f(n3,u)) = f(n3,f(n1,u)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c168,plain,
f(n3,f(n1,u)) = f(n3,f(n2,u)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
f(n2,f(n1,u)) = f(n3,f(n2,u)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c170,plain,
f(n3,f(n2,u)) = f(n2,f(n1,u)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c172,plain,
f(n2,f(n1,u)) = f(n2,f(n2,u)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
f(n2,f(n2,X2)) = f(u,f(n2,X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c174,plain,
f(n2,f(n2,X2)) = f(u2,f(u,X2)),
inference(transitivity,[status(thm)],[c173,c150]) ).
cnf(c175,plain,
f(n2,f(n2,u)) = f(u2,f(u,u)),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c177,plain,
f(u2,f(u,u)) = f(u2,uu),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
f(u2,uu) = v,
inference(transitivity,[status(thm)],[c160,c101]) ).
cnf(c179,plain,
f(u2,f(u,u)) = v,
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
f(n2,f(n2,u)) = v,
inference(transitivity,[status(thm)],[c175,c179]) ).
cnf(c181,plain,
f(n2,f(n1,u)) = v,
inference(transitivity,[status(thm)],[c172,c180]) ).
cnf(c182,plain,
f(n3,f(n2,u)) = v,
inference(transitivity,[status(thm)],[c170,c181]) ).
cnf(c183,plain,
f(n3,f(n1,u)) = v,
inference(transitivity,[status(thm)],[c168,c182]) ).
cnf(c184,plain,
f(n3,f(n3,u)) = v,
inference(transitivity,[status(thm)],[c166,c183]) ).
cnf(c185,plain,
f(n3,uu) = v,
inference(transitivity,[status(thm)],[c164,c184]) ).
cnf(c186,plain,
v = f(n3,uu),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
f(f(n3,X2),v) = f(f(n3,X2),f(n3,uu)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
f(n3,f(X2,uu)) = f(f(n3,X2),f(n3,uu)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c189,plain,
f(f(n3,X2),f(n3,uu)) = f(n3,f(X2,uu)),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
f(f(n3,X2),v) = f(n3,f(X2,uu)),
inference(transitivity,[status(thm)],[c187,c189]) ).
cnf(c191,plain,
f(f(n3,n2),v) = f(n3,f(n2,uu)),
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
uu = f(n3,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c193,plain,
f(n2,uu) = f(n2,f(n3,u)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
f(n2,f(n3,X2)) = f(f(n2,n3),f(n2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c195,plain,
f(n2,n3) = f(n2,f(n2,n1)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c196,plain,
f(f(n2,X2),n3) = f(f(n2,X2),f(n2,n1)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c197,plain,
f(n2,f(X2,n1)) = f(f(n2,X2),f(n2,n1)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c198,plain,
f(f(n2,X2),f(n2,n1)) = f(n2,f(X2,n1)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
f(f(n2,X2),n3) = f(n2,f(X2,n1)),
inference(transitivity,[status(thm)],[c196,c198]) ).
cnf(c200,plain,
f(f(n2,n2),n3) = f(n2,f(n2,n1)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
f(n2,f(n2,n1)) = f(f(n2,n2),n3),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c22]) ).
cnf(c203,plain,
f(f(n2,n2),n3) = f(u,n3),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
f(u,n3) = u3,
inference(symmetry,[status(thm)],[c6]) ).
cnf(c205,plain,
f(f(n2,n2),n3) = u3,
inference(transitivity,[status(thm)],[c203,c204]) ).
cnf(c206,plain,
f(n2,f(n2,n1)) = u3,
inference(transitivity,[status(thm)],[c201,c205]) ).
cnf(c207,plain,
f(n2,n3) = u3,
inference(transitivity,[status(thm)],[c195,c206]) ).
cnf(c208,plain,
f(f(n2,n3),f(n2,X2)) = f(u3,f(n2,X2)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
f(n2,f(n3,X2)) = f(u3,f(n2,X2)),
inference(transitivity,[status(thm)],[c194,c208]) ).
cnf(c210,plain,
f(n2,f(n3,u)) = f(u3,f(n2,u)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
f(u3,f(n2,u)) = f(u3,f(n1,u)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c212,plain,
f(u3,f(n1,u)) = f(u3,f(n3,u)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c213,plain,
f(u3,f(n3,u)) = f(u3,uu),
inference(congruence,[status(thm)],[c78]) ).
cnf(c214,plain,
f(u3,uu) = v,
inference(transitivity,[status(thm)],[c60,c101]) ).
cnf(c215,plain,
f(u3,f(n3,u)) = v,
inference(transitivity,[status(thm)],[c213,c214]) ).
cnf(c216,plain,
f(u3,f(n1,u)) = v,
inference(transitivity,[status(thm)],[c212,c215]) ).
cnf(c217,plain,
f(u3,f(n2,u)) = v,
inference(transitivity,[status(thm)],[c211,c216]) ).
cnf(c218,plain,
f(n2,f(n3,u)) = v,
inference(transitivity,[status(thm)],[c210,c217]) ).
cnf(c219,plain,
f(n2,uu) = v,
inference(transitivity,[status(thm)],[c193,c218]) ).
cnf(c220,plain,
f(n3,f(n2,uu)) = f(n3,v),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
v = f(n3,uu),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c222,plain,
f(n3,v) = f(n3,f(n3,uu)),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
f(n3,f(n3,uu)) = f(u3,f(u,uu)),
inference(substitution,[status(thm)],[c120]) ).
cnf(c224,plain,
f(u3,f(u,uu)) = f(u3,f(u3,uu)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c225,plain,
f(u3,f(u3,uu)) = f(u3,f(u1,uu)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c226,plain,
f(u3,f(u1,uu)) = f(u3,v),
inference(congruence,[status(thm)],[c101]) ).
cnf(c227,plain,
v = f(u1,uu),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c228,plain,
f(u3,v) = f(u3,f(u1,uu)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
f(u1,uu) = f(u3,uu),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c230,plain,
f(u3,f(u1,uu)) = f(u3,f(u3,uu)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
f(u3,uu) = f(u,uu),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c232,plain,
f(u3,f(u3,uu)) = f(u3,f(u,uu)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
f(u,f(n3,uu)) = f(u3,f(u,uu)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c234,plain,
f(u3,f(u,uu)) = f(u,f(n3,uu)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
uu = f(n3,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c236,plain,
f(n1,uu) = f(n1,f(n3,u)),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
f(n3,u) = f(n1,u),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c238,plain,
f(n1,f(n3,u)) = f(n1,f(n1,u)),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
f(n1,f(n1,X2)) = f(n2,f(n1,X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c240,plain,
f(n1,f(n1,X2)) = f(n3,f(n2,X2)),
inference(transitivity,[status(thm)],[c239,c40]) ).
cnf(c241,plain,
f(n1,f(n1,u)) = f(n3,f(n2,u)),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
f(n3,f(n2,u)) = f(n3,f(n1,u)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c243,plain,
f(n3,f(n1,u)) = f(n3,f(n3,u)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c244,plain,
f(n3,f(n3,u)) = f(n3,uu),
inference(congruence,[status(thm)],[c78]) ).
cnf(c245,plain,
f(n3,f(n1,u)) = f(n3,uu),
inference(transitivity,[status(thm)],[c243,c244]) ).
cnf(c246,plain,
f(n3,f(n2,u)) = f(n3,uu),
inference(transitivity,[status(thm)],[c242,c245]) ).
cnf(c247,plain,
f(n1,f(n1,u)) = f(n3,uu),
inference(transitivity,[status(thm)],[c241,c246]) ).
cnf(c248,plain,
f(n1,f(n3,u)) = f(n3,uu),
inference(transitivity,[status(thm)],[c238,c247]) ).
cnf(c249,plain,
f(n1,uu) = f(n3,uu),
inference(transitivity,[status(thm)],[c236,c248]) ).
cnf(c250,plain,
f(n3,uu) = f(n1,uu),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
f(u,f(n3,uu)) = f(u,f(n1,uu)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
f(u,f(n1,uu)) = f(u1,f(u,uu)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c253,plain,
f(u1,f(u,uu)) = f(u1,f(u3,uu)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c254,plain,
f(u1,f(u3,uu)) = f(u1,f(u1,uu)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c255,plain,
f(u1,f(u1,uu)) = f(u1,v),
inference(congruence,[status(thm)],[c101]) ).
cnf(c256,plain,
f(u1,f(u3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
f(u1,f(u,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c253,c256]) ).
cnf(c258,plain,
f(u,f(n1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c252,c257]) ).
cnf(c259,plain,
f(u,f(n3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c251,c258]) ).
cnf(c260,plain,
f(u3,f(u,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c234,c259]) ).
cnf(c261,plain,
f(u3,f(u3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c232,c260]) ).
cnf(c262,plain,
f(u3,f(u1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c230,c261]) ).
cnf(c263,plain,
f(u3,v) = f(u1,v),
inference(transitivity,[status(thm)],[c228,c262]) ).
cnf(c264,plain,
f(u3,f(u1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c226,c263]) ).
cnf(c265,plain,
f(u3,f(u3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c225,c264]) ).
cnf(c266,plain,
f(u3,f(u,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c224,c265]) ).
cnf(c267,plain,
f(n3,f(n3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c223,c266]) ).
cnf(c268,plain,
f(n3,v) = f(u1,v),
inference(transitivity,[status(thm)],[c222,c267]) ).
cnf(c269,plain,
f(n3,f(n2,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c220,c268]) ).
cnf(c270,plain,
f(f(n3,n2),v) = f(u1,v),
inference(transitivity,[status(thm)],[c191,c269]) ).
cnf(c271,plain,
f(f(n3,n2),f(u1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c162,c270]) ).
cnf(c272,plain,
f(f(n3,n2),f(u2,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c161,c271]) ).
cnf(c273,plain,
f(a,f(f(n3,n2),uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c144,c272]) ).
cnf(c274,plain,
f(a,f(n3,f(n2,u))) = f(u1,v),
inference(transitivity,[status(thm)],[c137,c273]) ).
cnf(c275,plain,
f(a,f(n3,f(n1,u))) = f(u1,v),
inference(transitivity,[status(thm)],[c129,c274]) ).
cnf(c276,plain,
f(a,f(n3,f(n3,u))) = f(u1,v),
inference(transitivity,[status(thm)],[c126,c275]) ).
cnf(c277,plain,
f(a,f(u3,f(u,u))) = f(u1,v),
inference(transitivity,[status(thm)],[c123,c276]) ).
cnf(c278,plain,
f(a,f(u3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c107,c277]) ).
cnf(c279,plain,
f(a,f(u1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c105,c278]) ).
cnf(c280,plain,
f(a,v) = f(u1,v),
inference(transitivity,[status(thm)],[c103,c279]) ).
cnf(c281,plain,
v = f(u1,uu),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c282,plain,
f(b,v) = f(b,f(u1,uu)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c284,plain,
f(b,f(u1,X2)) = f(f(u1,u3),f(u1,X2)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
f(u1,f(u3,X2)) = f(f(u1,u3),f(u1,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c286,plain,
f(f(u1,u3),f(u1,X2)) = f(u1,f(u3,X2)),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
f(b,f(u1,X2)) = f(u1,f(u3,X2)),
inference(transitivity,[status(thm)],[c284,c286]) ).
cnf(c288,plain,
f(b,f(u1,uu)) = f(u1,f(u3,uu)),
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
f(u1,f(u3,uu)) = f(u1,f(u1,uu)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c290,plain,
f(u1,f(u1,uu)) = f(u1,v),
inference(congruence,[status(thm)],[c101]) ).
cnf(c291,plain,
f(u1,f(u3,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
f(b,f(u1,uu)) = f(u1,v),
inference(transitivity,[status(thm)],[c288,c291]) ).
cnf(c293,plain,
f(b,v) = f(u1,v),
inference(transitivity,[status(thm)],[c282,c292]) ).
cnf(c294,plain,
f(u1,v) = f(b,v),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
f(a,v) = f(b,v),
inference(transitivity,[status(thm)],[c280,c294]) ).
cnf(c296,plain,
$false,
inference(resolution,[status(thm)],[c1,c295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 17:10:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.64 Command-line arguments: --no-flatten-goal
% 0.22/0.64
% 0.22/0.64 % SZS status Unsatisfiable
% 0.22/0.64
% 1.35/0.66 % SZS output start CNFRefutation
% See solution above
% 2.47/0.82
% 2.47/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------